O'Reilly noted that some in the media have said Trump was acting "unhinged" or "hysterical," but he thought the president was simply being defiant in a low-key way.

"Overall, I thought that he was in control," Wallace said. "And he seized control of the narrative and said, 'Chaos? Heck no. It's running like a [fine]-tuned machine."

He added that it's important not to exaggerate the importance of this news conference or the media's Trump coverage, because it all boils down to the results Trump gets as commander-in-chief.

"If he improves the economy, if he gets tax reform through, if he gets ObamaCare repealed and an effective [replacement] through, then it's not going to matter," Wallace said. "And conversely, if he doesn't get that stuff through and people's lives don't change, then he could have all the positive press in the world and it isn't going to matter."